Two-dimensional multi-timescale fully electromagnetic relativistic particle simulation is used to investigate relativistic electron heating in laser-produced plasmas. When laser pulses with peak intensities 1019 W cm−2 and different durations (e.g. 118 fs and 442 fs) are incident on overdense plasma slabs with step-like density profiles, the dynamics of plasmas and Fourier frequency spectra from our particle simulations demonstrate distinctly different properties in hot-electron temperatures, absorption, relativistic electron heating, and so on. The particular motions of the critical surfaces are discussed. From the two examples simulated in this paper, it is concluded that the interactions between plasmas and laser pulses with the same intensities and different durations are dominated by different mechanisms, which can lead to dissimilar dynamics of plasmas, relativistic heating, and so on.

Two-field fluid models for low-frequency density and electrostatic potential fluctuations in a purely toroidal magnetized low-β plasma are discussed. In particular, we present some simple models suitable for investigating plasma transport close to marginal stability. For gradient-driven fluctuations, linear normal mode analysis of the interchange and resistive drift wave instabilities are reviewed, with attention to the relative phase and amplitude of density and electrostatic potential fluctuations. This reveals many characteristic features of drift-wave fluctuations that are also observed in laboratory experiments and during ionospheric irregularities. Finally, these results are used to investigate the nonlinearly conserved energy functionals, discussing the effect of magnetic field curvature and particle collisions on energy, enstrophy, and cross-correlation between density and vorticity fluctuations. Implications for turbulent fluctuations and nonlinear transport in laboratory and ionospheric plasmas are discussed.

The stabilization of a viscous interface stressed by an oscillating magnetic field is investigated. Account is taken of the influence of free-surface currents on the effective solidly rotating fluid column. Only azimuthal modes are considered in the linear perturbation. The dispersion relation with or without free-surface currents is obtained in the form of a linear Mathieu equation with complex coefficients. It is found that there is a nonlinear relation between the surface current density and both the stratified viscosity and the stratified azimuthal magnetic field. The surface currents disappear on the interface of the fluid column when the stratified magnetic field has the value of unity. At this value, a coupled parametric resonance occurs in the absence of angular velocity. The magnetic field plays a stabilizing role. This role increases with increasing surface currents. The angular velocity plays a destabilizing role, while the field frequency plays a stabilizing role and acts against the angular velocity. The stratified viscosity plays a damping role in the presence of the surface current density, while, in the absence of a surface current, it plays two opposite roles corresponding to the presence or absence of the field frequency. A set of graphs are used to illustrate the relation between the presence of free-surface currents and both the viscosity and the azimuthal magnetic field.

It is shown that the interaction of dust with neutral plasma particles can lead to attractive forces between dust particles, both in the case where the distance between dust particles is less than the mean free path of neutral particles and in the case where it is greater. The expressions for attractive forces differs in the two limits only by a numerical coefficient. The additional force of dust interaction is found to be due to the neutrals created by recombination of charged plasma particles on the surface of dust particles. The influence of radiative dust cooling on dust–dust interaction is considered.

An analysis of the induction equation shows that the level surfaces of the magnetic field in a resistive plasma satisfy a certain bound upon the time means of their areas. When this bound is applied to some configurations typical of chaotic plasmas, it is shown that the number of bidimensional sheets where the field reaches a extremum is bounded, whereas the number of extremal ropes or points need not be. This also applies to current sheets.

The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas.

A rigorous theoretical investigation is made of obliquely propagating low-frequency electrostatic waves in a cylindrically bounded magnetized dusty plasma. A number of different modes, such as modified convective cells, coupled ion-cyclotron and dust-ion-acoustic waves, modified lower-hybrid waves, coupled dust-cyclotron and dust-acoustic waves, etc., are investigated. It is shown that the effects of the cylindrical boundary of the dusty plasma system, the external magnetic field, and the obliqueness (of the propagating modes) significantly modify the dispersion properties of these different low-frequency electrostatic waves. The implications of our results for laboratory dusty magnetoplasmas are briefly pointed out.

A numerical investigation of wave propagation in a magnetized plasma layer is performed. Four families of waves can propagate: plasma, cyclotron, anisotropic and waveguide modes. It is shown that the singular waves propagate at the crossing points of the waves with the complex zone boundary. The influence of the interface, the layer width and the magnetization of the plasma on the spectrum of the waves is analysed.

In recent years, numerical solutions of the equations of compressible magnetohydrodynamic (MHD) flows have been found to contain intermediate shocks for certain kinds of problems. Since these results would seem to be in conflict with the classical theory of MHD shocks, they have stimulated attempts to reexamine various aspects of this theory, in particular the role of dissipation. In this paper, we study the general relationship between the evolutionary conditions for discontinuous solutions of the dissipation-free system and the existence and uniqueness of steady dissipative shock structures for systems of quasilinear conservation laws with a concave entropy function. Our results confirm the classical theory. We also show that the appearance of intermediate shocks in numerical simulations can be understood in terms of the properties of the equations of planar MHD, for which some of these shocks turn out to be evolutionary. Finally, we discuss ways in which numerical schemes can be modified in order to avoid the appearance of intermediate shocks in simulations with such symmetry.

The orbital-motion-limited (OML) theory has been widely used to calculate the ion response to a charged grain immersed in plasma. The theory assumes there are no potential barriers preventing plasma ions from reaching positive-energy points in phase space. However, Allen et al. [J. Plasma Phys.63, 299 (2000)] have recently shown that for any finite-size negatively charged dust grain in a Maxwellian plasma, there are always potential barriers sufficient to exclude some ions. We calculate the magnitude of the potential barriers, and determine which ions are subject to barriers. The OML theory is shown to become exact in the limit of small grain size, and to be very accurate in calculating ion current to the grain for typical conditions pertinent to dusty plasma. Thus OML theory is well justified in calculating the floating potential. However, we find that potential barriers can influence the shielding of the potential at r ∼ λD under some conditions, especially large grams, high plasma density, and small Ti/Te.

The formation and propagation of ion phase-space vortices are observed in a numerical particle-in-cell simulation in two spatial dimensions and with three velocity components. The code allows for an externally applied magnetic field. The electrons are assumed to be isothermally Boltzmann-distributed at all times, implying that Poisson's equation becomes nonlinear for the present problem. Ion phase-space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam at the plasma boundary. We consider the effect of a finite beam diameter and a magnetic field, in particular. A vortex instability is observed, appearing as a transverse modulation, which slowly increases with time and ultimately breaks up the vortex. When many vortices are present at the same time, we find that it is their interaction that eventually leads to a gradual filling-up of the phase-space structures. The ion phase-space vortices have a finite lifetime, which is noticeably shorter than that found in one-dimensional simulations. An externally imposed magnetic field can increase this lifetime considerably. For high injected beam velocities in magnetized plasmas, we observe the excitation of electrostatic ion-cyclotron instabilities, but see no associated formation of ion phase-space vortices. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.

The path is sought in the temperature–density plane that allows desired plasma burning conditions to be reached in the shortest possible time. This task is undertaken using the tools of classical variational analysis. The derived expression of Euler's equation is found to be degenerate. Ways to overcome such an impasse are examined, and eventually the solution is obtained. Illustrative applications to the OMITRON proposed ignition experiment are presented, which make reference to the Lackner–Gottardi and ITER-P89 scalings for the energy confinement time.

Radiofrequency heating in toroidal geometry is described. Starting from a general theory, expressions for the dielectric response and the radiofrequency diffusion operator are obtained. The computationally most efficient simplified expressions bear a close resemblance to the results of uniform plasma theory, but differ from them in their interpretation. In cases where the simplified expressions do not describe the physics faithfully, more general but computationally slower ones are available. Rigorously accounting for the geometry and the wave field yields fine structure that is commonly overlooked. Aside from causing the well-known k∥-upshift or downshift impacting on the Doppler shift, the non-zero poloidal magnetic field modifies the orbital topology and forces one to account for the poloidal inhomogeneity of the static magnetic field. The expressions obtained restore intuition on how an electric field interacts with a charged particle, but, in so doing, cast doubt on the degree of realism of predictions of simplified models that do not account for the constructive or destructive interference phenomena introduced by the orbital topology non-uniformity. The expressions represent a numerical challenge, but show the necessity for the detailed description: the ‘coarse-graining’ underlying simplified models yields a result that has the right order of magnitude for interference related to crosstalk between resonances or multiple encounters with a given resonance, but may be an order of magnitude wrong for predictions on the combined effect of a poloidal mode spectrum. A Fokker–Planck code BATCH (Bounce-Averaged Tool for Cyclotron Heating), relying on the expressions obtained, is presented and some results are discussed.

A numerical investigation of anisotropic waves propagating in a magnetized plasma layer is performed. In gyrotropic plasma layers, there are two regions in which electromagnetic waves exist owing to the anisotropic properties of the plasma. Mainly these are Rayleigh pseudosurface waves. In the upper anisotropic region, a wave exists only in a planar waveguide. In the lower anisotropic region, there are two waves. The dispersion and the origin of these waves are analysed. The distribution of the energy and the Poynting vector are unique, and they differ from those of other families of electromagnetic waves. At small wavenumbers, the energy is concentrated in one of the dielectrics and at large wavenumbers, it is concentrated in the plasma.

The nature of stationary-wave structures in multi-ion plasmas with differential streaming between the ions is elucidated by making use of the concept of a generalized sonic point for such plasmas and the Bernoulli equation for each flowing ion species. It is shown that the Bohm criterion for the existence of solitons and double layers is an expression of either the supersonic nature of the collective ion flow or the subsonic nature of individual ion flows. From the perspective of the dispersion equation for stationary waves, both of these requirements, and hence the Bohm criterion, merely ensure that the wave is evanescent, rather than sinusoidal, which, in turn, ensures that the system can evolve nonlinearly. The structure of the ion flows in these transitions is determined by the Bernoulli equation, a fundamental property of which is that the ion plasma energy exhibits a minimum where the ion flow speed equals the local ion sound speed. This implies that for positive flowing ions, a positive change in electric potential induces a deceleration (pile-up) if the flow is supersonic or an acceleration (spread-out) if the flow is subsonic. This feature limits the maximum strength of the potential in a soliton, and sheds light on the underlying reason why double layers can only exist in very special circumstances without the introduction of additional trapped or reflected particle populations.

The Korteweg–de Vries–Zakharov–Kuznetsov (KdV–ZK) equation, governing the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external uniform magnetic field in a non-thermal plasma, admits soliton solutions having a sech2 profile. The higher-order growth rates of instability are obtained using the method developed by Allen and Rowlands [J. Plasma Phys.50, 413 (1993); 53, 63 (1995)]. The growth rate of instability is obtained correct to order k2, where k is the wavenumber of a long-wavelength plane-wave perturbation. The case where the coefficient of the nonlinear term in the KdV–ZK equation vanishes is also considered.

A hydrodynamic approach is employed to study a cosmic-ray–plasma system, which comprises thermal plasma, cosmic rays and two oppositely propagating Alfvén waves. The hydrodynamic approach is a good approximation in dealing with the structure or dynamics of the system. In this paper, we concentrate on the steady-state structures of the system, in particular, structures with continuous (or smooth) profiles. Three mechanisms are responsible for the energy exchange between different components. They are work done by plasma flow via pressure gradients, cosmic-ray streaming instability and stochastic acceleration. The interplay between these mechanisms generates several morphologically different structures. They may be divided into two categories: one looks like the test-particle picture and the other looks like a modified shock. Very often the profiles are non-monotonic, which is in sharp contrast to systems with only thermal plasma and cosmic rays, whose flow velocity (and cosmic-ray pressure) profiles are always monotonically decreasing (and increasing).

We investigate the nature of stationary structures streaming at subfast magnetosonic speeds perpendicular to the magnetic field in a bi-ion plasma consisting of protons and a heavy ion species in which the magnetic field is frozen into the electrons, whose inertia may be neglected. The study is based on the properties of the structure equation for the system, which is derived from the equations of motion and the Maxwell equations, and therefore reflects the coupling between the two ion fluids and the electrons through the Lorentz forces and charge neutrality. The basic features of the structure equation are elucidated by making use of conservation of total momentum and charge neutrality, which provide relations between the ion speeds in the unperturbed flow direction and the electron speed. This combination of relations, which we call the momentum hodograph of the system, reveals the structure of the flow and the magnetic field in a solitary-type pulse. In particular, we find that in the initial portion of a compressive soliton, heavy ions run ahead of the electrons and the protons lag between them until a point is reached where they all once more attain the same speed, after which the protons run ahead and are accelerated whereas the heavies now lag behind the continuously decelerating electrons. The second half of the wave is a mirror image of the first portion. The strength of the compression (the amplitude of the wave) is determined from the momentum hodograph, and depends upon the initial Mach number, abundance ratio of heavies to protons and the mass ratio. The analysis is relevant to subfast flows of mass-loaded plasmas and pile-up boundaries, which appear near comets and non-magnetic planets.

By means of the cold-electron fluid equations, we deduce a new strongly nonlinear surface solitary-wave solution for a semi-infinite plasma.